The State Department's top Senate appropriator said Tuesday he would be willing to advance an emergency supplemental to address the crisis of Syrian refugees.

Sen. Lindsey Graham, the chairman of the Appropriations Subcommittee on State and Foreign Operations, said if the United States does not change course with respect to accepting refugees, the country might as well "take the Statue of Liberty and tear it down."

At a National Press Club luncheon, the South Carolina Republican said an approach that does not involve the U.S. taking refugees would mean the statue, featuring the quote from Emma Lazarus, "Give me your tired, your poor, your huddled masses yearning to breathe free," would no longer belong in New York harbor.

As for how to pay for the refugee issue, Graham said he would favor taking the steps needed to increase funding levels, blaming the current situation on the budget deal that resulted in the sequester. Graham has been supportive of reaching a big budget agreement, including changes to entitlement programs, though emergency spending is often not offset.

"I would support an emergency appropriation for refugees. You spend now or you spend later. I'm going to sit down with Sen. Leahy and see if we can find some money to help the international refugee associations and [the United Nations] particularly who are doing a good job trying to manage this," Graham said. "I don't just want to pick a number. I don't know how many we should take, I don't know how much money we should spend, but I know we should take our fair share and we need to spend more to get ahead of this."

Graham, who is running for president, is taking a different approach than one of his rivals, Sen. Ted Cruz of Texas. In a statement Tuesday, Cruz said "if the ultimate goal is to return [migrants] to their homes, which I believe it should be, it doesn't make sense from a logistical or a security standpoint to move large numbers of them to far-off countries like the United States."

White House Press Secretary Josh Earnest told reporters Tuesday the Obama administration was considering additional steps to deal with the crisis. He said no one has proposed the United States take in "hundreds of thousands" of additional refugees.

It was not yet clear what, if anything, the White House might request from Capitol Hill.